%0 Journal Article
%T One parameter families of Legendrian torus knots
%A Tam¨¢s K¨¢lm¨¢n
%J Mathematics
%D 2004
%I arXiv
%X We compute the Chekanov-Eliashberg contact homology of what we call the Legendrian closure of a positive braid. We also construct an augmentation for each such link diagram. Then we apply the monodromy techniques established in an earlier paper to a certain natural loop in the space L' of positive Legendrian (p,q) torus knots to show that L' has a nontrivial fundamental group, which is mapped non-injectively into the fundamental group of K by the map induced by inclusion (here, K is the space of all smooth positive (p,q) torus knots). This is the first example that Legendrian and classical knots behave differently at the level of one parameter families.
%U http://arxiv.org/abs/math/0409005v1